The Finn held his nerve and fended off a late attack from the Ferrari racer to take the win by just six-tenths of a second.
Valtteri made a lightning getaway - a start so good that the FIA investigated it to ensure it was not a jump start - to lead off the line and then built up a strong lead from Vettel in the first stint. The Ferrari came back at him in the second half of the race, as Valtteri struggled with a blistered tyre, but he had just enough left to cross the line first for the win.
"That champagne tasted good," said Valtteri. "The first win is obviously special, but this is only my second win, so it's a great feeling to get it. It's been my best weekend yet with the pole and the win and I hope we can continue from here.
"The start was absolutely perfect - definitely my best start ever. And you saw how close it was with Sebastian at the end, so today I needed it. The car was so good this weekend, so I knew we could still do it.
"I got a massive blister on the rear-left in the second stint after just five laps, which made the car tricky to drive. I was losing more and more performance, but it wasn't my first time having to keep Sebastian behind me. I kept my focus and managed to finish the race without any mistakes. It would have been tricky to keep Sebastian behind for much longer, so it was good to see the chequered flag.
"I'm still in the title fight and I'm only going to get better. We're growing all the time."